In the Multiresolution Modifier there is a way to save the mutliresolution information, but how do I import and apply the saved *.btx file?
The way I know it works is by saving displacements into one .btx file, creating another .btx file on another model and substituting the latter with the former.


Save needed sculpt and name the .btx file appropiately ("useful-sculpt.btx").
Open new file (or create another model in the same one). On another model add Multires modifier and set it to the same level of subdivision.
While this isn't necessary in order the method to work it's best to keep the same subdivision level so not to lose any details from the original sculpt.
Save sculpt of second model with Save External button to a temporary .btx file (note: do not overwrite the first one).
The step is present only to make accessible button for opening a file.
Press small folder icon next to the file name in Multires modfiier's properties of the second model to open file browser and choose there file with original sculpt ("useful-sculpt.btx").